Geometric dimension of groups for the family of virtually cyclic subgroups
Geometric dimension of groups for the family of virtually cyclic subgroups
By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality ℵ n admits a finite‐dimensional classifying space with virtually cyclic stabilizers of dimension n + h + 2 . We also provide a criterion for groups that fit into an extension with torsion‐free quotient to admit a finite‐dimensional classifying space with virtually cyclic stabilizers. Finally, we exhibit examples of integral linear groups of type F whose geometric dimension for the family of virtually cyclic subgroups is finite but arbitrarily larger than the geometric dimension for proper actions. This answers a question posed by W. Lück.
697-726
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
September 2014
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Degrijse, Dieter and Petrosyan, Nansen
(2014)
Geometric dimension of groups for the family of virtually cyclic subgroups.
Journal of Topology, 7 (3), .
(doi:10.1112/jtopol/jtt045).
Abstract
By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality ℵ n admits a finite‐dimensional classifying space with virtually cyclic stabilizers of dimension n + h + 2 . We also provide a criterion for groups that fit into an extension with torsion‐free quotient to admit a finite‐dimensional classifying space with virtually cyclic stabilizers. Finally, we exhibit examples of integral linear groups of type F whose geometric dimension for the family of virtually cyclic subgroups is finite but arbitrarily larger than the geometric dimension for proper actions. This answers a question posed by W. Lück.
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e-pub ahead of print date: 30 December 2013
Published date: September 2014
Organisations:
Mathematical Sciences
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Local EPrints ID: 360933
URI: http://eprints.soton.ac.uk/id/eprint/360933
ISSN: 1753-8416
PURE UUID: e4a13cd6-1faa-4de1-aefb-b799e62b29d3
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Date deposited: 09 Jan 2014 11:25
Last modified: 15 Mar 2024 03:49
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Author:
Dieter Degrijse
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